Determination of the masses of planetary satellites from their mutual gravitational perturbations

We analyze the possibility of determining the masses of outer planetary satellites from their mutual gravitational perturbations via ground-based observations. Such a technique has been applied in (Emelyanov, 2005b) to determine the mass of the Jovian satellite Himalia. In this paper, we use the least-squares method to compute the errors of satellite masses inferred from simulated observations. We analyze several of the most suitable variants of groups of outer satellites of planets with maximum mutual attraction. We found that the mass of the Satumian satellite Phoebe (S9) can be refined by continuing observations of the satellite S25 Mundilfari until 2027. We show that the masses of other known outer planetary satellites cannot be determined from ground-based observations.     

Generation of a secular system in the analytical theory for the motion of the moon

In order to generate an analytical theory of the motion of the Moon by considering planetary perturbations, a procedure of general planetary theory (GPT) is used. In this case, the Moon is considered as an addition planet to the eight principal planets. Therefore, according to the GPT procedure, the theory of the Moon’s orbital motion can be presented in the form of series with respect to the evolution of eccentric and oblique variables with quasi-periodic coefficients, which are the functions of mean longitudes for principal planets and the Moon. The relationship between evolution variables and the time is determined by a trigonometric solution for the independent secular system that describes the secular motion of a perigee and the Moon node by considering secular planetary inequalities. Principal planetary coordinates required for generating the theory of the motion of the Moon includes only Keplerian terms, the intermediate orbit, and the linear theory with respect to eccentricities and inclinations in the first order relative to the masses. All analytical calculations are performed by means of the specialized echeloned Poisson Series Processor EPSP.     

Global dynamics of the Gliese 876 planetary system

The Gliese 876 planetary system consists of two Jupiter-like planets having a nearly commensurate 2:1 orbital periods ratio. Because the semimajor axes of the planets are very small (of the order 0.1 au and 0.2 au, respectively), and the eccentricity of the inner companion is ≃0.3, the mutual perturbations are extremely large. However, many authors claim the long-term orbital stability of the system, at least over 500 Myr for initial conditions found by Rivera & Lissauer. Results of investigations of a migration of initially separated planets into the close 2:1 mean motion resonance lock from Lee & Peale also support the conclusion that the system should be stable for the lifetime of the parent star. Initial conditions of the system, found from non-linear N -body fits by Laughlin & Chambers and Rivera & Lissauer, to the radial velocity curve, formally allow for a variety of orbital configurations of the GJ 876 system, e.g. coplanar, with planetary inclinations in the range [≃30°, 90°], and with relative inclinations of orbital planes as high as 80°. Our work is devoted to the stability investigation of the systems originating from the fitted initial conditions. We study neighbourhoods of these initial states in the orbital parameter space. We found estimations of the 2:1 mean motion resonance width and dynamical limitations on the planetary masses. We also obtain a global representation of the domains of the orbital parameters space in which initial conditions leading to stable evolutions can be found. Our results can be useful in localization of the best, stable fits to the observational data. In our investigations we use the MEGNO technique (the Mean Exponential Growth factor of Nearby Orbits) invented by Cincotta & Simó. It allows us to distinguish efficiently and precisely between chaotic and regular behaviour of a planetary system.     

The influence of mutual perturbations on the eccentricity excitation by jet acceleration in extrasolar planetary systems

We study the influence of mutual planetary perturbations on the process of eccentricity excitation by jet acceleration suggested by Namouni (Astron. J. 130, 280–294). Modeling the jet’s action by a constant-direction acceleration, we solve the linear secular equations of the combined planetary perturbations and the jet acceleration of the host star for a two-planet system. The effects of the acceleration’s strength, relative mass ratio and the relative distance of the two planets are investigated. The model is applied to the extrasolar planetary systems of HD 108874, 47 Uma, and HD 12661.     

Planetary perturbations of the Moon in ELP 2000

A new solution for the planetary perturbations of the Moon is being built in the frame of ELP 2000, using Bretagnon's planetary theories, and achieved at the first order. It contains the two actions commonly distinguished: direct and indirect. The internal precision of computation is 2×10^–6 arcsec. First-order planetary perturbations, in the direct case (Venus & Mars), have been compared to Standaert's solution. The major discrepancy reaches 70 cm in the longitude of Venus. Perturbations of the second order with respect to planetary masses, have been undertaken and illustrations are given. Finally, new values for the perigee and node motions are proposed.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.     

Analytical direct planetary perturbations on the orbital motion of satellites

An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit.     

Alternative representation of planetary perturbations

An attempt is made to find a representation of planetary perturbations which does not require a Fourier expansion. For the planetary type three body problem a sequence of canonical transformations is given based on Landen transformations coupled with a rescaling of the time. The expansion is carried out to the order 2 in the Hamiltonian.     

Expansion of the planetary Hamiltonian function

We expand the planetary Hamiltonian function with its two parts, the principal and the indirect, up to the seventh order in the planetary masses. We adopt the Jacobi-Radau system of origins. The expansiion is valid for any number of planets.     

Terrestrial planet and asteroid formation in the presence of giant planets. I. Relative velocities of planetesimals subject to Jupiter and Saturn perturbations.

We investigate the orbital evolution of 10(13)- to 10(25) -g planetesimals near 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolution when the mutual perturbations between the planetesimals become important. We include nebular gas drag and the effects of Jupiter and Saturn at their present masses and in their present orbits. Gas drag introduces a size-dependent phasing of the secular perturbations, which leads to a pronounced dip in encounter velocities (Venc) between bodies of similar mass. Plantesimals of identical mass have Venc approximately 1 and approximately 10 m s-1 (near 1 and 2.6 AU, respectively) while bodies differing by approximately 10 in mass have Venc approximately 10 and approximately 100 m s-1 (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, will occur only by collisions of bodies of nearly the same mass. There will be essentially no gravitational focusing between bodies less than 10(22) to 10(25) g, allowing growth of planetary embryos in the terrestrial planet region to proceed in a slower nonrunaway fashion. The environment in the asteroid belt will be even more forbidding and it is uncertain whether even the severely depleted present asteroid belt could form under these conditions. The perturbations of Jupiter and Saturn are quite sensitive to their semi-major axes and decrease when the planets' heliocentric distances are increased to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit formation of a system of terrestrial planet embryos on a approximately 10(6)-year timescale, initially by nonrunaway growth and transitioning to runaway growth after approximately 10(5) years. The calculations reported here are valid under the condition that the relative velocities of the bodies are determined only by Jupiter and Saturn perturbations and by gas drag, with no mutual perturbations between planetesimals. If, while subject to these conditions, the bodies become large enough for their mutual perturbations to influence their velocity and size evolution significantly, the problem becomes much more complex. This problem is under investigation.     

Effects of Planetary Migration on Natural Satellites of the Outer Planets

Numerous studies in the past few years have analyzed possible effects of planetary migration on the small bodies of the Solar System (mainly asteroids and KBOs), with the double aim of explaining certain dynamical structures in these systems, as well as placing limits on the magnitude of the radial migration of the planets. Here we undertake a similar aim, only this time concentrating on the dynamical stability of planetary satellites in a migration scenario. However, different from previous works, the strongest perturbations on satellite systems are not due to the secular variation of the semimajor axes of the planets, but from the planetesimals themselves. These perturbations result from close approaches between the planetesimals and satellites.We present results of several numerical simulations of the dynamical evolution of real and fictitious satellite systems around the outer planets, under the effects of multiple passages of a population of planetesimals representing the large-body component of a residual rocky disk. Assuming that this component dominated the total mass of the disk, our results show that the present systems of satellites of Uranus and Neptune do not seem to be compatible with a planetary migration larger than even one quarter that suggested by previous studies, unless these bodies were originated during the late stage of evaporation of the planetesimal disk. For larger variations of the semimajor axes of the planets, most of the satellites would either be ejected from the system or suffer mutual collisions due to excitation in their eccentricities. For the systems of Jupiter and Saturn, these perturbations are not so severe, and even large migrations do not introduce large instabilities.Nevertheless, even a small number of 1000-km planetesimals in the region may introduce significant excitation in the eccentricities and inclinations of satellites. Adequate values of this component may help explain the present dynamical distribution of distant satellites, including the highly peculiar orbit of Nereid.     

Planetary perturbations on the Libration of the Moon

A theory of the libration of the Moon, completely analytical with respect to the harmonic coefficients of the lunar gravity field, was recently built (Moons, 1982). The Lie transforms method was used to reduce the Hamiltonian of the main problem of the libration of the Moon and to produce the usual libration series p₁, p₂ and . This main problem takes into account the perturbations due to the Sun and the Earth on the rotation of a rigid Moon about its center of mass. In complement to this theory, we have now computed the planetary effects on the libration, the planetary terms being added to the mean Hamiltonian of the main problem before a last elimination of the angles. For the main problem, as well as for the planetary perturbations, the motion of the center of mass of the Moon is described by the ELP 2000 solution (Chapront and Chapront-Touze, 1983).     

A numerical-analytical method for studying the orbital evolution of distant planetary satellites

We describe an approximate numerical-analytical method for calculating the perturbations of the elements of distant satellite orbits. The model for the motion of a distant satellite includes the solar attraction and the eccentricity and ecliptic inclination of the orbit of the central planet. In addition, we take into account the variations in planetary orbital elements with time due to secular perturbations. Our work is based on Zeipel’s method for constructing the canonical transformations that relate osculating satellite orbital elements to the mean ones. The corresponding transformation of the Hamiltonian is used to construct an evolution system of equations for mean elements. The numerical solution of this system free from rapidly oscillating functions and the inverse transformation from the mean to osculating elements allows the evolution of distant satellite orbits to be studied on long time scales on the order of several hundred or thousand satellite orbital periods.     

Resonant Periodic Motion and the Stability of Extrasolar Planetary Systems

Families of nearly circular periodic orbits of the planetary type are studied, close to the 3/1 mean motion resonance of the two planets, considered both with finite masses. Large regions of instability appear, depending on the total mass of the planets and on the ratio of their masses.Also, families of resonant periodic orbits at the 2/1 resonance have been studied, for a planetary system where the total mass of the planets is the 4% of the mass of the sun. In particular, the effect of the ratio of the masses on the stability is studied. It is found that a planetary system at this resonance is unstable if the mass of the outer planet is smaller than the mass of the inner planet.Finally, an application has been made for the stability of the observed extrasolar planetary systems HD82943 and Gliese 876, trapped at the 2/1 resonance.     

A new method of initial orbit determination

Up to now we have been dealing with the construction of entirely analytical planetary theories such as VSOP82 (Bretagnon, 1982) and TOP82 (Simon, 1983). These theories take into account the whole of the Newtonian perturbations of nine point masses: the Sun, the Earth-Moon barycentre, the planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune. They also take into account perturbations due to some minor planets, to the action of the Moon and the relativistic effects. The perturbations of these last three types are in a very simple way under analytical form but they considerably increase the computations when introduced in the numerical integration programs.In the present paper we thus study a solution in which the Newtonian perturbations for the ten point masses are treated through numerical integration, the other perturbations being analytically added.     

On the expansions of intermediate orbit for general planetary theory

Intermediate orbit for general planetary theory is constructed in the form of multivariate Fourier series with numerical coefficients. The structure and efficiency of the derived series are illustrated by giving various statistical properties of the coefficients.The ability of the recently proposed elliptic function approach to compress the Fourier series representing the intermediate orbit is investigated. Our results confirm that when mutual perturbations of a pair of planets are considered the elliptic function approach is quite efficient and allows one to compress the series substantially. However, when perturbations of three or more planets are under study the elliptic function approach does not give any advantages.     

Analytical Planetary solution VSOP2000

The analytical planetary solution VSOP2000 determines the planetary perturbations with the help of an iterative method from a solution developed till the third order of the disturbing masses. This solution is from 10 to 100 times more precise than the previous analytical solutions VSOP82 and VSOP87, at the level of some 0.1mas for Mercury, Venus and the Earth and some mas for the other planets over the timespan 1900–2000.With this solution, the relation between the Barycentric Coordinate Time (TCB) and the Geocentric Coordinate Time (TCG) is computed with an accuracy better than 0.1 nanosecond over the interval 1965–2015. We also determined the contribution to the Eulerian angles of the geodetic precession-nutation.     

Colours and Composition of the Centaurs

Centaurs are widely believed to come from the Edgeworth-Kuiper belt, located beyond the orbit of Neptune. From here they can be injected into the inner part of the Solar System through planetary perturbations or mutual collisions. Due to their origin and dynamical evolution, Centaurs are supposed to constitute a transition population of objects from the large reservoir of Trans-Neptunian Objects (TNOs) to the active bodies of the inner Solar System. On the basis of the present knowledge of the physical properties of Centaurs and TNOs a similarity between the two populations appears evident. This is the strongest observational constraint supporting the theory of common origin.     

A numerical investigation on the eccentricity growth of GNSS disposal orbits

We present the results of an extensive numerical exploration performed on the eccentricity growth in MEO associated with two possible end-of-life disposal strategies for GNSS satellites. The study calls attention to the existence of values of initial inclination, longitude of ascending node, and argument of perigee that are more advantageous in terms of long-term stability of the orbit. The important role of the initial epoch and a corresponding periodicity are also shown. The present investigation is influential in view of recent analytical and numerical developments on the chaotic nature of the region due to lunisolar perturbations, but also for the upcoming Galileo and BeiDou constellations.     

Dynamics of Planetary Satellites in the Solar System

After the discovery of a huge number of satellites around Jupiter, Saturn, and Uranus, it is necessary to collect together information about all of the planetary satellite systems and to define the possible classification of objects and types of their motion. We give physical parameters of the satellites: their masses, sizes, apparent magnitudes in opposition, and geometrical albedos. We present some of the orbital quantities that characterize the orbits, their shapes and orientation in space, as well as data on the rotation of satellites. The emphasis is on the peculiarities of their motion—the forces acting on them, the main orbital perturbations, and the influence of commensurabilities in the mean motions of satellites. We list references to the main theories of their motion.     

Symmetric and asymmetric 3:1 resonant periodic orbits with an application to the 55Cnc extra-solar system

We study the dynamics of 3:1 resonant motion for planetary systems with two planets, based on the model of the general planar three body problem. The exact mean motion resonance corresponds to periodic motion (in a rotating frame) and the basic families of symmetric and asymmetric periodic orbits are computed. Four symmetric families bifurcate from the family of circular orbits of the two planets. Asymmetric families bifurcate from the symmetric families, at the critical points, where the stability character changes. There exist also asymmetric families that are independent of the above mentioned families. Bounded librations exist close to the stable periodic orbits. Therefore, such periodic orbits (symmetric or asymmetric) determine the possible stable configurations of a 3:1 resonant planetary system, even if the orbits of the two planets intersect. For the masses of the system 55Cnc most of the periodic orbits are unstable and they are associated with chaotic motion. There exist however stable symmetric and asymmetric orbits, corresponding to regular trajectories along which the critical angles librate. The 55Cnc extra-solar system is located in a stable domain of the phase space, centered at an asymmetric periodic orbit.